How to Implement
the New Math Standards, Part I
Arlyne LeSchack
The
New York State Board of Regents revised the New York State Mathematics
Standards this past March 2005. At every level of school, New
York State teachers of Mathematics have to provide students
with the knowledge and understanding of mathematics necessary
to function in the world. 

Instructionally,
this translates into a goal with three components:
 Conceptual
Understanding
 Procedural
Fluency
 Problem Solving
Conceptual
Understanding
This consists of those relationships constructed internally and
connected to already existing ideas. It involves the understanding
of mathematical ideas and procedures and includes the knowledge
of the basic arithmetic facts. Students use conceptual understanding
of mathematics when they identify and apply principles, know and
apply facts and definitions and compare and contrast related concepts.
Further, knowledge learned with understanding provides the foundation
for remembering mathematical methods and for solving new problems.
Procedural
Fluency
This is the skill to carry out procedures flexibly and accurately.
It includes algorithms, the step by step routines needed to perform
the four arithmetic operations. Procedural fluency applies to other
areas of mathematics as well, like the ability to use a protractor
for measuring the size of an angle or how to use a calculator. Calculators
are encouraged because if used properly they can enhance a students
understanding and computing skills. With understanding, a students
is less likely to make common computational errors. In the past,
this might have been called having "number sense."
Problem Solving
Problem solving is the ability to formulate, represent and solve
mathematical problems. Problems generally fall into three types:
one step problems, multistep problems and process problems. Most
problems that we encounter in the real world are multistep or process
problems. In order to solve them, we have to integrate both conceptual
understanding and procedural fluency.
But just knowing
a concept or a procedure is not useful. Students must be taught
how to analyze a problem and how to choose the most useful strategy
to solve the problem. This means exposing the students to a broad
range of strategies. Sometimes selecting a strategy is the most
difficult part of the solution, so mathematics instruction must
include when to apply certain strategies as well as how to apply
a strategy.
Click
here to read the next installment, process and content strands
of the new standards.
If you have
comments or questions, please contact me at aleschack@aol.com.
